Axial stress & strain worksheet with answers

Free printable Axial stress & strain worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
300 kNØ30110 GPaØ100/50500 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 50 mm, E = 110 GPa). Both are 500 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 110 GPaL = 500 mm
σr = MPa
2.Easy
Ø 25 mm1 mP = 90 kN

A solid round bar carries an axial tensile load P. Find the normal stress σ in the bar.

P = 90 kNd = 25 mm
σ = MPa
3.Medium
P = ?12400 mm400 mmØ25Ø50δ = 0.2 mm

A bar is made of a steel segment (diameter 25 mm, length 400 mm, E = 200 GPa) joined end to end with a segment made of copper (diameter 50 mm, length 400 mm, E = 120 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.2 mm in total.

segment 1: steel, Ø25 mm, 400 mm, E = 200 GPasegment 2: copper, Ø50 mm, 400 mm, E = 120 GPaδ = 0.2 mm
P = kN
4.Medium
Ø 30 mmBrass3 mP = 45 kN

Find the elongation δ of the brass bar under the axial load.

P = 45 kNd = 30 mmL = 3 mE = 100 GPa
δ = mm
5.Hard
Ø 35 mmAluminium2 mØ 12 mmSteel0.5 mP = 75 kN

The stepped bar is fixed at the wall and loaded at its free end. Find the total elongation δ.

P = 75 kNsegment 1: Ø35 mm, 2 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 0.5 m, steel (E = 200 GPa)
δ = mm
6.Hard
Ø 30 mmAluminium1 mØ 16 mmCopper0.5 mP = 65 kN

The stepped bar is fixed at the wall and loaded at its free end. Find the largest normal stress σmax in the bar.

P = 65 kNsegment 1: Ø30 mm, 1 m, aluminium (E = 70 GPa)segment 2: Ø16 mm, 0.5 m, copper (E = 117 GPa)
σmax = MPa

Answer key

  1. 1. σr = 76.01 MPa
  2. 2. σ = 183.3 MPa
  3. 3. P = 34.65 kN
  4. 4. δ = 1.91 mm
  5. 5. δ = 3.885 mm
  6. 6. σmax = 323.3 MPa

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